How do you find the inverse of $f (x) = 3 (2^{x})$ $f(x) =3(2^x)$ ?

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Answer 1 · 2015-11-27T17:06:16

$y = \frac{ln (x) - ln (3)}{ln (2)}$ $y=(ln(x)-ln(3))/ln(2)$

Write as $. . y = 3 (2^{x})$ $color(white)(..) y=3(2^x)$

Take logs

$ln (y) = ln (3) + ln (2^{x})$ $ln(y)=ln(3)+ln(2^x)$

But $. . ln (2^{x}) = x ln (2)$ $color(white)(..)ln(2^x)=xln(2)$ giving:

$ln (y) = ln (3) + x ln (2)$ $ln(y)=ln(3)+xln(2)$

$x = \frac{ln (y) - ln (3)}{ln (2)}$ $x=(ln(y)-ln(3))/ln(2)$

Swap $x and y$ $x " and " y$ around giving:

$y = \frac{ln (x) - ln (3)}{ln (2)}$ $y=(ln(x)-ln(3))/ln(2)$

How do you find the inverse of f(x)=3(2x)f(x) =3(2^x)?